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Constructions preserving the associative and the commutative laws

Published online by Cambridge University Press:  09 April 2009

A. Shafaat
A. Shafaat
Affiliation:
Département de Mathématiques Faculté des Sciences, Université Laval, Québec G1K 7P4, Canada.
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Abstract

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The associative and the commutative laws are characterized by preservation under the construction of powers and addition of a (new) unit element. This is used to generate the varieties defined by the two laws from two element groupoids.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1976 , pp. 112 - 117
Copyright
Copyright © Australian Mathematical Society 1976

References

Bleicher, M. N., Schneider, H. and Wilson, R. L. (1973), ‘Permanence of identities on algebras’, Algebra Universalis 3, 72–93.CrossRefGoogle Scholar
Cohn, P. M. (1965), Universal Algebra (Harper and Row, New York, 1965).Google Scholar
Whitney, S. (to appear), Model classes of linear theories.Google Scholar
Shafaat, A. (to appear), Power algebras of free algebras.Google Scholar